Pam  00:00

Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.

Kim  00:06

And I'm Kim.

Pam  00:07

And this is a... What are you laughing about?

Kim  00:09

I'm laughing because you say, "Let's go!" "Like, wait. Where? Wait! Wait for me!" 

Pam  00:14

"Where are we going?!" Where we chat about our math strategies. Every Wednesday evening, I throw out a math problem on social media, and people from around the world chat about the strategies they use, and comment on each other's thinking.

Kim  00:25

Okay, so this week, our problem was... Good gravy. 48 times 52. How would you solve this problem? Pause the podcast. Solve it yourself however you'd like. The problem is 48 times 52.

Pam  00:41

You know, we actually do believe in that. The more that you mess around with relationships, the better our strategies will hang on what you've already been thinking about. So, just to throw that out there.

Kim  00:51

And it's super fun when somebody will say, "I did it like you!" So, you know, there's this idea that you thought about it first, and then when you read other people's thinking, then you can honestly say, "I did it like you!"

Pam  01:07

Yeah. Yeah, that's kind of cool. 

Kim  01:09

Alright, I'm going to first. 

Pam  01:12

What are you doing? 

Kim  01:13

48 makes me think of 50, which makes me think of 100,  so I am going to write down 100 times. 52 is 5200. Half of that is 2600. And that would be fifty 52s. And then I'm going to subtract two 52s, which is 104. So, I've got 2600 minus 104. So, 2496.

Pam  01:38

Nice. I like it. Would you ever consider doing fifty 48s, and then adding on two more 48s.

Kim  01:48

Say it again? Fifty 48s.

Pam  01:50

Mmhm. And then... So, fifty 48s, you could do kind of similar to what you did.

Kim  01:55

Yeah, if I did a hundred 48s and fifty 48s.

Pam  01:57

Yeah.

Kim  01:57

Sure, sure. 

Pam  01:58

And then you would just subtract two 48s. No, sorry. Add two 48s. And the two 48s is that 96 sitting there in that 2,496.

Kim  02:08

I like it. 

Pam  02:09

Okay cool. 

Kim  02:09

Is that what you did? 

Pam  02:10

No!

Kim  02:11

Oh. Okay.

Pam  02:11

No, I was just playing with. But we could have.

Kim  02:14

Sure.

Pam  02:15

But I didn't. No, so I'm still playing around with the idea that these problems are... What? There's a number right in the middle of them. 50. So, 48, 52. 50 is right in the middle.

Kim  02:27

Mmhm. 

Pam  02:27

So, I could think about 48 as 50 minus 2, and I could think about 50 as 50 plus 2, and I could multiply all those parts together. So, 50 times 50 is 2500 or 2,500. The -2 times 50 and the positive 2 times 50 add to 0. -2 times -2 is 4, so I have to subtract 4. 2,500 subtract 4 is 2,400 and there's that 96. Da dum dum. So, I could have said to myself, "The number in between them is 50, so it's just going to be 50^2 minus the difference 2^2." I could have done that. Because if I have a minus b times a plus b, that's always going to be a^2 minus b^2. So, if I can figure out what the a and the b are, in this case 50 and 2, then I could do that. Do I want to do that? It's good question. 

Kim  03:22

Well, what's really nice is, if you think about it like 50^2, you can actually draw the square. 

Pam  03:28

That's true.

Kim  03:29

And then you can find...

Pam  03:32

That overlapping...

Kim  03:33

Yeah.

Pam  03:34

...b^2 that has to be taken off? 

Kim  03:36

Yeah. 

Pam  03:37

That is pretty cool. Nice spatial representation.

Kim  03:40

Mmhm. Okay, well, we can't wait to see every week what you do. Join us on MathStratChat and let us know how you think about the problems. Comment on each other's strategies.

Pam  03:49

We'll post the problems on Wednesday around 7:00 pm Central. And when you answer, tag me and use the hashtag MathStratChat. Then join us here to hear how we're thinking about the problem. Thanks for being part of the Math is Figure-Out-Able movement! Math is Figure-Out-Able!